Conventional xerographic copiers do not render faithful or pleasing copies of continuous tone originals. The usual discharge characteristics of the photoconductor and solid area developability of the xerographic development system combine to yield a Tone Reproduction Curve (TRC) with a steep slope and a narrow range. An ideal TRC is a 45.degree. line. The result of the nonideal Xerographic TRC is a copy having washed out highlights and overdeveloped shadows. In order to produce a more faithful and pleasing copy, halftoning algorithms have been developed to yield a TRC with a lower slope and extended range of input gray scale that produces a corresponding change in the output.
In halftoning processes employed by xerographic based digital printers, the image is formed of a texture pattern of black and white spots that gives the impression of gray when viewed at normal reading distance. If the halftone frequency and number of distinguishable half-tone steps are both sufficiently high, the printed picture will be pleasing to the eye. Halftone methods employed in xerographic printers have traditionally been binary, that is, the laser writes with only two laser intensity levels: on and off.
When assessing the quality of a binary xerographic printer, there are two key measures: the halftone frequency (i.e., the number of halftone cells per linear inch), and the number of distinguishable gray steps. To produce a copy of a picture with a minimally acceptable degree of halftone screen visibility requires at least 65 halftone cells per inch measured along a diagonal of the page (assuming a 45 degree halftone screen). Good quality halftones require about 100 cells/inch, while high quality magazines typically use 150 cells/inch or higher.
The number of distinct gray steps needed in the pictorial copy depends on the eye's ability to distinguish closely spaced grays. It has been found that the human eye, at normal reading distance, can detect a reflectance modulation of about 0.5% at spatial frequencies near 1 cy/mm. The inverse of this just perceptible modulation has been interpreted as the maximum number of gray steps that the eye can perceive. A rule of thumb in the printing industry is that an acceptable picture should contain about 65 gray steps. For good quality, 100 or more steps are desired. However, in a binary printer, the maximum number of output gray steps is limited to the number of pixels per halftone cell (p), plus 1. Thus, for a typical 8.times.4 rectangular halftone cell, p+1=33 output gray steps. High halftone frequencies have fewer pixels per cell and therefore produce fewer gray steps. This is a fundamental limitation of digital binary printers.
Hybrid halftoning is a pictorial printing technique employing a halftone cell structure similar to conventional binary halftoning, but with the added degree of freedom afforded by the use of multilevel gray pixels. U.S. Pat. No. 4,868,587, entitled "Image Halftoning System for Printers", to Loce et al., the disclosure of which is incorporated by reference herein, discloses a hybrid halftoning system. U.S. Pat. No. 4,868,587 discloses the use of a multilevel laser to expose pixels at more than two levels of exposure (i.e. more than just on and off). Alternatively, different colored toners can be used to produce black and gray pixels, respectively, which are combined to form the output image. The resulting multilevel charge pattern is then developed to produce a high quality pictorial print. Using multilevel pixels as opposed to binary pixels results in a substantially greater number of unique halftone cells. When properly selected the average reflectance of these cells can be arrayed nearly uniformly along a perceived lightness scale. To obtain these optimal cells, specific gray pixel levels are used. With specific gray pixel levels, hybrid halftoning can yield significantly improved pictorial reproduction, when compared to binary halftoning, at greatly reduced resolution and data rates. FIG. 1 illustrate that similar tone reproduction quality is obtained with a 1350 spots per inch (spi) binary halftone scheme (FIG. 1) as is obtained using a 300 spi, four level hybrid halftone (FIG. 1) employing all 165 possible cells. Both cases have the same halftone screen frequency (i.e., cell size), and the tone reproduction curves have about the same number of steps. As is apparent, the resolution and data rate advantages of the hybrid approach are significant in this idealized case.
The hybrid halftone system described above is idealized in the sense that it is assumed that the xerographic printer is capable of creating the specific gray pixel reflectance values and that xerographic noise is low enough such that areas of predominantly gray pixels may be formed. However, in most xerographic systems, large gray areas tend to show objectionable artifacts due to nonuniformities of the xerographic process. For example, periodic banding due to photoconductor velocity variations or raster output scanner (ROS) polygon wobble is a common and serious problem in xerographic laser printers.